The use of vibronic sensors for determining physical variables is widely distributed in automation technology—especially in process automation technology and in manufacturing automation technology. The oscillatable element of a vibronic sensor is connected by material-bonding and/or by force interlocking, e.g. frictional interlocking, with a membrane and can be embodied as any kind of oscillatory fork or as a single rod. The membrane and the oscillatable element connected with the membrane, thus the oscillatable unit, are/is excited via a transmitting/receiving unit to execute oscillations. The transmitting/receiving unit is usually at least one piezoelectric, respectively electromechanical, element. Moreover, also so-called membrane oscillators are known, in the case of which the oscillatable element is composed only of a membrane.
Usually, a vibronic sensor is excited via an analog electronics to execute oscillations, wherein the analog electronics together with the oscillatable unit form the analog oscillatory circuit. Corresponding vibronic sensors, respectively vibronic measuring devices, are manufactured and sold in various embodiments by the applicant under the marks, LIQUIPHANT and SOLIPHANT.
Vibronic sensors enable detection of a process-specific parameter, such as the limit-level of a liquid or a solid in a container. Usually, for detection of a predetermined fill level (limit level), the sensor is operated with the resonant frequency of the oscillatable unit. By detecting the frequency change at a set phase of usually 90°, it can be detected whether the oscillatable unit is in contact with the medium or whether it is oscillating freely.
Moreover, it is known to determine, respectively to monitor, other process specific parameters in a medium by evaluating the oscillatory behavior of vibronic sensors. These process-specific parameters include especially the density and the viscosity, however, also the temperature, of the medium. For the purpose of determining the density of a liquid medium, the phase difference (often also referred to simply as phase) between the input signal and the output signal is set to 45° or −135°. In setting this phase difference, a frequency change is unequivocally attributable to a change of the density of the medium, since an influencing by the viscosity of the fluid medium can be excluded. Published International Patent Application WO 02/031471 A2 describes an apparatus for viscosity measurement. Known from European Patent EP 2 041 529 B1 is an apparatus for determining the density of a liquid medium.
As evident based on the above mentioned examples, an analog electronics has the disadvantage that it is relatively inflexible. Especially, the analog electronics must be matched to each sensor, respectively sensor type, as a function of its oscillation characteristics and further as a function of the respective application—thus whether the sensor is to be applied for fill level-, density- or viscosity measurement. A solution, which avoids the above mentioned disadvantages, is described in applicant's German Application DE 10 2012 113 045.0, filed on Dec. 12, 2012. The content of DE 10 2012 113 045.0 is incorporated here by reference.
The portfolio of vibronic sensors is quite variant rich. Examples of this are the products of the applicant manufactured and sold under the marks, LIQUIPHANT and SOLIPHANT. Thus, it can be stated that known and future sensors do and will differ relatively strongly as concerns their geometry. In the case of the solution proposed in DE 10 2012 113 045.0, for the purpose of analytical determining the interaction between the oscillatable unit embodied as an oscillatory fork and the fluid medium, the two fork tines of the oscillatory fork are approximated via a mathematical model. In the concrete case, the two fork tines are approximated mathematically as ideal elliptical cylinders.
In order to transfer the method known from DE 10 2012 113 045.0 to oscillatable units with a different geometry, it is necessary to modify the mathematical model correspondingly. In such case, it is to be noted that the mathematical description of the interaction, respectively the interaction, between the oscillatable unit and the medium is relatively complex. Added to this are two other considerations:                due to the complex geometry of the oscillatable unit, there are always small discrepancies between the modeled and the real situation; and        the geometries of the oscillatable units of a sensor type, e.g. LIQUIPHANT T or LIQUIPHANT M, are usually, e.g. due to manufacturing tolerances, never one hundred percent in agreement.        
Both aspects act unfavorably on the desired high accuracy of measurement of vibronic sensors.